Ohio’s State Tests · of operations to perform multi-digit arithmetic. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers,

Ohio’s State Tests

ITEM RELEASE

SPRING 2018

GRADE 4MATHEMATICS

i (2018)

Table of Contents Content Summary and Answer Key ............................................................................... iii Question 7: Question and Scoring Guidelines .............................................................. 1 Question 7: Sample Responses ....................................................................................... 5 Question 11: Question and Scoring Guidelines .......................................................... 11 Question 11: Sample Responses ................................................................................... 15 Question 12: Question and Scoring Guidelines ......................................................... 25 Question 12: Sample Responses ................................................................................... 29 Question 15: Question and Scoring Guidelines .......................................................... 35 Question 15: Sample Responses ................................................................................... 39 Question 16: Question and Scoring Guidelines .......................................................... 49 Question 16: Sample Responses ................................................................................... 51 Question 17: Question and Scoring Guidelines .......................................................... 57 Question 17: Sample Response .................................................................................... 60 Question 18: Question and Scoring Guidelines .......................................................... 61 Question 18: Sample Responses ................................................................................... 65 Question 24: Question and Scoring Guidelines .......................................................... 73 Question 24: Sample Response .................................................................................... 75 Question 26: Question and Scoring Guidelines .......................................................... 77 Question 26: Sample Responses ................................................................................... 81 Question 27: Question and Scoring Guidelines .......................................................... 91 Question 27: Sample Responses ................................................................................... 95 Question 29: Question and Scoring Guidelines ........................................................ 105 Question 29: Sample Response .................................................................................. 107 Question 30: Question and Scoring Guidelines ........................................................ 109 Question 30: Sample Responses ................................................................................. 113 Question 31: Question and Scoring Guidelines ........................................................ 123 Question 31: Sample Response .................................................................................. 125

ii (2018)

Question 32: Question and Scoring Guidelines ........................................................ 127 Question 32: Sample Response .................................................................................. 129 Question 34: Question and Scoring Guidelines ........................................................ 131 Question 34: Sample Responses ................................................................................. 135 Question 37: Question and Scoring Guidelines ........................................................ 145 Question 37: Sample Responses ................................................................................. 149 Question 39: Question and Scoring Guidelines ........................................................ 159 Question 39: Sample Responses ................................................................................. 163 Question 44: Question and Scoring Guidelines ........................................................ 169 Question 44: Sample Response .................................................................................. 171 Question 47: Question and Scoring Guidelines ........................................................ 173 Question 47: Sample Response .................................................................................. 175 Question 48: Question and Scoring Guidelines ........................................................ 177 Question 48: Sample Responses ................................................................................. 181

iii (2018)

Grade 4 Math Spring 2018 Item Release

Content Summary and Answer Key Question

No.* Item Type

Content Cluster

Content Standard

Answer Key Points

7 Equation Item

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. (4.MD.2)

--- 1 point

11 Equation Item

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. (4.NF.4) b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)

--- 1 point

12 Equation Item

Geometric measurement: understand concepts of angle and measure angles.

Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. (4.MD.6)

--- 1 point

* The question number matches the item number in the Item Level Report in the Online Reporting System. The items are numbered sequentially in the practice site.

iv (2018)



No.* Item Type

Content Cluster

Content Standard

Answer Key Points

15 Table Item

Use the four operations with whole numbers to solve problems.

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (4.OA.3)

--- 1 point

16 Equation Item

Use place value understanding and properties of operations to perform multi-digit arithmetic.

Fluently add and subtract multi-digit whole numbers using the standard algorithm. (4.NBT.4)

--- 1 point

17 Multiple Choice

Geometric measurement: understand concepts of angle and measure angles.

Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: (4.MD.5) b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

A 1 point


v (2018)



No.* Item Type

Content Cluster

Content Standard

Answer Key Points

18 Matching Item

Extend understanding of fraction equivalence and ordering.

Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (4.NF.2)

--- 1 point

24 Multiple Choice

Understand decimal notation for fractions, and compare decimal fractions.

Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. (4.NF.7)

D 1 point

26 Graphic Response

Understand decimal notation for fractions, and compare decimal fractions.

Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. (4.NF.5)

--- 1 point


vi (2018)



No.* Item Type

Content Cluster

Content Standard

Answer Key Points

27 Equation Item


Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ... (4.MD.1)

--- 1 point

29 Multiple Choice

Use the four operations with whole numbers to solve problems.

Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (4.OA.2)

A 1 point

30 Equation Item


Understand a fraction a/b with a > 1 as a sum of fractions 1/b. (4.NF.3) d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

--- 1 point


vii (2018)



No.* Item Type

Content Cluster

Content Standard

Answer Key Points

31 Multiple Choice

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. (4.G.2)

D 1 point

32 Multi-Select Item


Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. (4.MD.3)

A, C, E 1 point

34 Graphic Response Item

Use place value understanding and properties of operations to perform multi-digit arithmetic.

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (4.NBT.5)

--- 1 point

37 Graphic Response Item

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. (4.G.1)

--- 1 point


viii (2018)



No.* Item Type

Content Cluster

Content Standard

Answer Key Points

39 Equation Item

Generalize place value understanding for multi-digit whole numbers.

Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. (4.NBT.2)

--- 1 point

44 Multi-Select Item

Gain familiarity with factors and multiples.

Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. (4.OA.4)

A, C, E, F 1 point

47 Multiple Choice

Represent and interpret data.

Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. (4.MD.4)

A 1 point

48 Equation Item


Understand a fraction a/b with a > 1 as a sum of fractions 1/b. (4.NF.3) c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

--- 1 point


1 (2018)

Grade 4 Math

Spring 2018 Item Release

Question 7

Question and Scoring Guidelines

2 (2018)

Question 7

28237 20512

Points Possible: 1

Content Cluster: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

Content Standard: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. (4.MD.2)

3 (2018)

Scoring Guidelines Exemplar Response

• 198

Other Correct Responses

• Any equivalent value

For this item, a full-credit response includes:

• A correct value (1 point).

5 (2018)

Grade 4 Math


Question 7

Sample Responses

6 (2018)

Sample Response: 1 point

Notes on Scoring

This response earns full credit (1 point) because it identifies the correct number of minutes that Brian was at the movie theater.

• The student may draw a number line and use a strategy likecounting on to find the total number of minutes.

60 + 60 + 60 + 18

= 120 + 60 + 18

= 180 + 18

= 198 minutes

7 (2018)


Notes on Scoring This response earns full credit (1 point) because it identifies the correct number of minutes that Brian was at the movie theater.

• The student may draw a number line and use a strategy like counting on to find an equivalent value to the total number of minutes.

60.00 + 60.00 + 60.00 + 18.00

= (3 × 60.00) + 18.00

= 180.00 + 18.00

= 198.00 minutes

8 (2018)

Sample Response: 0 points

Notes on Scoring

This response earns no credit (0 points) because it identifies an incorrect number of minutes that Brian was at the movie theater.

• The student may correctly determine that Brian was at themovie theater for 3 hours and 18 minutes, but incorrectlyinterprets 3 hours as 3 minutes, and 18 minutes as 0.18minute.

4: 18 − 1: 00 3: 18

3:18 ≠ 3.18 minutes

1:00 p.m. to 4:18 p.m. ≠ 3.18 minutes

9 (2018)


Notes on Scoring This response earns no credit (0 points) because it identifies an incorrect number of minutes that Brian was at the movie theater.

• The student may forget that Brian was still at the movies for 18 minutes after 4:00pm.

60 + 60 + 60

= 120 + 60

= 180 minutes

1:00 p.m. to 4:18 p.m. ≠ 180 minutes

11 (2018)

Grade 4 Math


Question 11


12 (2018)

Question 11

29193 20512

Points Possible: 1

Content Cluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Content Standard: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. (4.NF.4) b. Understand a multiple of a/b as a multiple of 1/b, and use thisunderstanding to multiply a fraction by a whole number. Forexample, use a visual fraction model to express 3 × (2/5) as 6 × (1/5),recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)

13 (2018)


• 15





15 (2018)

Grade 4 Math


Question 11

Sample Responses

16 (2018)


17 (2018)

Notes on Scoring This response earns full credit (1 point) because it identifies a missing value that correctly completes the equation.

• The student may model the left side of the equation as 45 of 3 whole

units shaded, and recognize the product is 12 unit fractions of 15.

= 125

45 × 3 = 12

5 AND 12 × 1

5 = 12

5

45 × 3 = 12 × 1

5

18 (2018)


19 (2018)

Notes on Scoring This response earns full credit (1 point) because it identifies a missing value that correctly completes the equation.

• The student may use multiplication to find the product of 45 × 3 as 12

5

and recognize 12 × 15 is equal to 12

5 before giving their answer as a

fraction equivalent to 15.

45 × 3 = 12

5 AND 12

5 = 12 ×

= 15 SINCE 12

5 = 12 × 1

5

15 × 2

2 = 2

10

20 (2018)


21 (2018)

Notes on Scoring This response earns no credit (0 points) because it identifies an incorrect missing value in the equation.

• The student may multiply 45 by 3

3 instead of by 3

1 and identify an

incorrect missing value based on the error. 45 × 3

3 = 12

15 AND 12

15 = 12 ×

= 115

SINCE 1215

= 12 × 115

AND 45 × 3

3 = 12

15

45 × 3 ≠12 × 1

15

22 (2018)


23 (2018)

Notes on Scoring This response earns no credit (0 points) because it identifies an incorrect missing value in the equation.

• The student may correctly calculate the product of 45 × 3 as 12

5 and

then multiply the right side of the equation by 125

instead of using it to identify the missing value. 45 × 3 = 12

5

12 × 125

= 1445

45 × 3 ≠ 12 × 144

5

25 (2018)

Grade 4 Math


Question 12


26 (2018)

Question 12

27449 20512

Points Possible: 1

Content Cluster: Geometric measurement: understand concepts of angle and measure angles.

Content Standard: Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. (4.MD.6)

27 (2018)


• 142




• The correct number (1 point).

29 (2018)

Grade 4 Math


Question 12

Sample Responses

30 (2018)


Notes on Scoring

This response earns full credit (1 point) because it identifies the correct measure of the angle, in degrees.

• The student uses the correct scale on the protractor tomeasure the angle.

31 (2018)


Notes on Scoring This response earns full credit (1 point) because it identifies the correct measure of the angle, in degrees.

• The student finds a measure equivalent to 142 degrees.

32 (2018)


Notes on Scoring

This response earns no credit (0 points) because it identifies an incorrect measure of the angle, in degrees.

• The student may round the degree value of the angleto the nearest labeled degree.

33 (2018)


Notes on Scoring This response earns no credit (0 points) because it identifies an incorrect measure of the angle, in degrees.

• The student may use the incorrect scale on the protractor to measure the angle.

35 (2018)

Grade 4 Math


Question 15


36 (2018)

Question 15

28774 20512

Points Possible: 1

Content Cluster: Use the four operations with whole numbers to solve problems.

Content Standard: Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (4.OA.3)

37 (2018)



• Any three integers S, M, L for which 7𝑆𝑆 + 11𝑀𝑀 + 13𝐿𝐿 = 100


• A correct table (1 point).

39 (2018)

Grade 4 Math


Question 15

Sample Responses

40 (2018)


41 (2018)

Notes on Scoring This response earns full credit (1 point) because it identifies a correct combination of posters that the teacher could have bought for $100.

• The student may use a table to find a combination of $7, $11, and $13 posters that total $100.

28 + 33 + 39 = (28 + 33) + 39 = (61) + 39

= 100

42 (2018)


43 (2018)

Notes on Scoring This response earns full credit (1 point) because it identifies a correct combination of posters that the teacher could have bought for $100.

• The student may use a table to find a combination of $7, $11, and $13 posters that total $100.

21 + 66 + 13 = 21 + 13 + 66 = (21 + 13) + 66 = (34) + 66

= 100

44 (2018)


45 (2018)

Notes on Scoring This response earns no credit (0 points) because it identifies an incorrect combination of posters that the teacher could have bought for $100.

• The student may use a table to choose values for the posters that total less than $100 instead of exactly $100.

70 + 11 + 13 = 70 + (11 + 13) = 70 + (24) = 94 94 ≠ 100

46 (2018)


47 (2018)

Notes on Scoring This response earns no credit (0 points) because it identifies an incorrect combination of posters that the teacher could have bought for $100.

• The student may use a table to choose values for the posters that total less than $100 instead of exactly $100.

0 + 33 + 65 = 33 + 65 = 98 98 ≠ 100

49 (2018)

Grade 4 Math


Question 16


50 (2018)

Question 16

24349 20512


• 21,631





Points Possible: 1

Content Cluster: Use place value understanding and properties of operations to perform multi-digit arithmetic.

Content Standard: Fluently add and subtract multi-digit whole numbers using the standard algorithm. (4.NBT.4)

51 (2018)

Grade 4 Math


Question 16

Sample Responses

52 (2018)


Notes on Scoring

This response earns full credit (1 point) because it identifies the correct difference between 34,162 and 12,531.

• The student may subtract 12,531 from 34,162.

3 34,162– 1 2,531 2 1,631

53 (2018)


Notes on Scoring This response earns full credit (1 point) because it identifies the correct difference between 34,162 and 12,531 using an algorithm.

• The student finds a correct equivalent value of 21,631. 3 34,162.00 – 1 2,531.00

2 1,631.00

54 (2018)


Notes on Scoring This response earns no credit (0 points) because it identifies an incorrect value as the difference between 34,162 and 12,531.

• The student may add the two numbers instead of subtracting them. 34,162 + 12,531 46,693 34,162 – 12,531 ≠ 46,693

55 (2018)


Notes on Scoring This response earns no credit (0 points) because it identifies an incorrect difference between 34,162 and 12,531.

• The student may subtract the 1 hundred in 34,162 from the 5-hundreds in 12,531 instead of regrouping.

34,162 – 12,531 22,431 34,162 – 12,531 ≠ 22,431

57 (2018)

Grade 4 Math


Question 17


58 (2018)

Question 17

29289

Points Possible: 1

Content Cluster: Geometric measurement: understand concepts of angle and measure angles.

Content Standard: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: (4.MD.5) b. An angle that turns through n one-degree angles is said to havean angle measure of n degrees.

59 (2018)

Scoring Guidelines Rationale for Option A: Key – The student correctly chooses the angle whose measure is between 90 and 180 degrees. Rationale for Option B: This is incorrect. The student may confuse the definition of acute angles and obtuse angles, thinking that an obtuse angle is an angle whose measure is between 0 and 90 degrees. Rationale for Option C: This is incorrect. The student may think that an obtuse angle is an angle whose measure is greater than 90 degrees, and choose the largest angle. However, an obtuse angle is an angle whose measure is between 90 and 180 degrees. Rationale for Option D: This is incorrect. The student may think that an obtuse angle is an angle whose measure is greater than 180 degrees, and choose the smallest angle whose measure matches this definition.

60 (2018)


61 (2018)

Grade 4 Math


Question 18


62 (2018)

Question 18

25518 20512

Points Possible: 1

Content Cluster: Extend understanding of fraction equivalence and ordering.

Content Standard: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (4.NF.2)

63 (2018)



• N/A


• A correct table (1 point).

65 (2018)

Grade 4 Math


Question 18

Sample Responses

66 (2018)


67 (2018)

Notes on Scoring This response earns full credit (1 point) because it identifies the correct comparison for each fraction.

• The student may use a model to compare each fraction to 34.

68 (2018)


69 (2018)

Notes on Scoring This response earns no credit (0 points) because it identifies an incorrect comparison for one of the fractions.

• The student may use a number line to correctly compare 610

and 912

to 34.

• The student may use a number line and incorrectly compare 45 to 3

4

because they are close together on the number line.

70 (2018)


71 (2018)

Notes on Scoring This response earns no credit (0 points) because it identifies incorrect comparisons for two fractions.

• The student may use a number line to correctly compare 610

to 34.

• The student may use a number line and incorrectly compare 45 and

912

to 34.

73 (2018)

Grade 4 Math


Question 24


74 (2018)

Question 24

27402

Points Possible: 1

Content Cluster: Understand decimal notation for fractions, and compare decimal fractions.

Content Standard: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. (4.NF.7)

75 (2018)

Scoring Guidelines Rationale for Option A: This is incorrect. The student may think that the inequality symbol was read as “greater than”. Rationale for Option B: This is incorrect. The student may identify that the value contains a 9, which is larger than 8, but did not consider the place value. Rationale for Option C: This is incorrect. The student may choose an equivalent value. Rationale for Option D: Key – The student correctly identifies that 0.9 is greater than 0.8.


77 (2018)

Grade 4 Math


Question 26


78 (2018)

Question 26

27248

79 (2018)

20512

Points Possible: 1 Content Cluster: Understand decimal notation for fractions, and compare decimal fractions. Content Standard: Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. (4.NF.5)

80 (2018)



• Any 40 boxes selected for Part A


• A correct model and equation (1 point).

81 (2018)

Grade 4 Math


Question 26

Sample Responses

82 (2018)


83 (2018)

Notes on Scoring This response earns full credit (1 point) because it shows the correct number of boxes on the hundreds grid and identifies the correct fraction that makes the equation true.

84 (2018)


85 (2018)

Notes on Scoring This response earns full credit (1 point) because it shows the correct number of boxes on the hundreds grid and identifies the correct fraction that makes the equation true.

86 (2018)


87 (2018)

Notes on Scoring This response earns no credit (0 points) because it shows a fraction that does not make the equation true.

• In Part B, the student may think that because the denominator adds another 0 (the digit in the ones place in the denominator) to the end of the number, then the numerator should have another 4 (the digit in the ones place in the numerator) added to the end of the number.

88 (2018)


89 (2018)

Notes on Scoring This response earns no credit (0 points) because it shows an incorrect number of boxes on the hundreds grid. In Part A, the student selects 5 columns rather than 4.

91 (2018)

Grade 4 Math


Question 27


92 (2018)

Question 27

25109 20512

Points Possible: 1


Content Standard: Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ... (4.MD.1)

93 (2018)


• 9,000





95 (2018)

Grade 4 Math


Question 27

Sample Responses

96 (2018)


97 (2018)

Notes on Scoring This response earns full credit (1 point) because it identifies the correct number of meters that the student ran.

• The student may use a table to correctly convert from kilometers to meters.

98 (2018)


99 (2018)

Notes on Scoring This response earns full credit (1 point) because it identifies the correct number of meters that the student ran.

• The student may identify that 1 km =1000 m and multiply 9 by 1,000 to find the number of meters in 9 kilometers.

100 (2018)


101 (2018)

Notes on Scoring This response earns no credit (0 points) because it identifies an incorrect number of meters that the student ran.

• The student may use a table and divide by 1000 instead of multiplying by 1000.

While decimals are introduced in the standards in grade 4, division at this grade is limited to whole number quotients and remainders with up to four-digit dividends and one-digit divisors.

102 (2018)


103 (2018)

Notes on Scoring This response earns no credit (0 points) because it identifies an incorrect number of meters that the student ran.

• The student may think that there are only 100 meters in 1 kilometer.

105 (2018)

Grade 4 Math


Question 29


106 (2018)

Question 29

24714

Points Possible: 1 Content Cluster: Use the four operations with whole numbers to solve problems. Content Standard: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (4.OA.2)

107 (2018)

Scoring Guidelines Rationale for Option A: Key – The student correctly identifies the number of cupcakes that Sarah made. Rationale for Option B: This is incorrect. The student may think “times as many” represents subtraction. Rationale for Option C: This is incorrect. The student may think “times as many” represents addition. Rationale for Option D: This is incorrect. The student may multiply 30 and 3 rather than dividing.


109 (2018)

Grade 4 Math


Question 30


110 (2018)

Question 30

25763 20512

Points Possible: 1


Content Standard: Understand a fraction a/b with a > 1 as a sum of fractions 1/b. (4.NF.3) d. Solve word problems involving addition and subtraction offractions referring to the same whole and having like denominators,e.g., by using visual fraction models and equations to represent theproblem.

111 (2018)


• 16




• The correct fraction (1 point).

113 (2018)

Grade 4 Math


Question 30

Sample Responses

114 (2018)


115 (2018)

Notes on Scoring This response earns full credit (1 point) because it identifies the correct difference between the fraction of muffins that Eric ate and the fraction of muffins that Nancy ate.

• The student may use a length model to subtract 36 from 4

6.

116 (2018)


117 (2018)

Notes on Scoring This response earns full credit (1 point) because it identifies the correct difference between the fraction of muffins that Eric ate and the fraction of muffins that Nancy ate.

• The student may use a model to find an equivalent value to 16.

118 (2018)


119 (2018)

Notes on Scoring This response earns no credit (0 points) because it identifies an incorrect difference between the fraction of muffins that Eric ate and the fraction of muffins that Nancy ate.

• The student may calculate the difference of the whole number of muffins eaten rather than the fraction (of the pan) of muffins eaten.

4 – 3 = 1 46 – 3

6 ≠ 1

120 (2018)


121 (2018)

Notes on Scoring This response earns no credit (0 points) because it identifies an incorrect difference between the fraction of muffins that Eric ate and the fraction of muffins that Nancy ate.

• The student may think they need to add to find the difference, so they add the numerators together and add the denominators together instead of using subtraction.

36 + 4

6 ≠ 7

12

123 (2018)

Grade 4 Math


Question 31


124 (2018)

Question 31

29448

Points Possible: 1

Content Cluster: Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Content Standard: Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. (4.G.2)

125 (2018)

Scoring Guidelines Rationale for Option A: This is incorrect. The student may think that right angles are also acute angles and thus think all shapes in each group have at least one acute angle. Rationale for Option B: This is incorrect. The student may think right angles are obtuse angles, then see that most of the shapes in Group 2 have obtuse angles, but does not check all of them. Rationale for Option C: This is incorrect. The student may recognize that all of the figures in Group 1 have at least one pair of parallel sides and that 3 shapes in Group 2 have at least 1 pair of parallel sides but does not check all of the shapes. Rationale for Option D: Key – The student correctly recognizes that the groups are sorted by figures that have perpendicular sides and those that do not.


127 (2018)

Grade 4 Math


Question 32


128 (2018)

Question 32

23525

Points Possible: 1


Content Standard: Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. (4.MD.3)

129 (2018)

Scoring Guidelines Rationale for First Option: Key – The student correctly identifies a model for the garden having an area of 24 square feet. Rationale for Second Option: This is incorrect. The student may select a model having a perimeter of 24 feet. Rationale for Third Option: Key – The student correctly identifies a model for the garden having an area of 24 square feet. Rationale for Fourth Option: This is incorrect. The student may select a model having a perimeter of 24 feet. Rationale for Fifth Option: Key – The student correctly identifies a model for the garden having an area of 24 square feet.


131 (2018)

Grade 4 Math


Question 34


132 (2018)

Question 34

25711 20512

Points Possible: 1

Content Cluster: Use place value understanding and properties of operations to perform multi-digit arithmetic.

Content Standard: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (4.NBT.5)

133 (2018)



• Any correct model that represents 312


• A correct model (1 point).

135 (2018)

Grade 4 Math


Question 34

Sample Responses

136 (2018)


137 (2018)

Notes on Scoring This response earns full credit (1 point) because it represents the correct product of 156 and 2.

• The student may multiply 156 by 2 to get 312 and then place models in the blank box that represent 312.

156

× 2 = 156

× 2

200 = 100 × 2

100 = 50 × 2

+ 12 = 6 × 2

312

138 (2018)


139 (2018)

Notes on Scoring This response earns full credit (1 point) because it represents a correct product of 156 and 2.

• The student creates a model of 2 groups of 156, using repeated addition to represent the product of 156 and 2.

156 × 2 = 156

+ 156

312

140 (2018)


141 (2018)

Notes on Scoring This response earns no credit (0 points) because it represents an incorrect product of 156 and 2.

• The student may misread the question and represent 156 instead of 156 × 2.

156 × 2 ≠ 156

142 (2018)


143 (2018)

Notes on Scoring This response earns no credit (0 points) because it represents an incorrect product of 156 and 2.

• The student may add 2 to 156 instead of multiplying.

156 × 2 ≠ 158

145 (2018)

Grade 4 Math


Question 37


146 (2018)

Question 37

24801 20512

147 (2018)

Points Possible: 1 Content Cluster: Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Content Standard: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. (4.G.1)

148 (2018)



• Any quadrilateral with only one set of parallel sides


• A correct figure (1 point).

149 (2018)

Grade 4 Math


Question 37

Sample Responses

150 (2018)


151 (2018)

Notes on Scoring This response earns full credit (1 point) because it identifies a quadrilateral with only one set of parallel sides.

• The student draws a trapezoid that has only one set of parallel sides.

152 (2018)


153 (2018)

Notes on Scoring This response earns full credit (1 point) because it identifies a quadrilateral with only one set of parallel sides.

• The student draws a trapezoid that has only one set of parallel sides.

While square corners (right angles) are not required to be drawn as part of a response, students in grades 3–5 can still earn full credit if they include square corners as part of a correct response.

154 (2018)


155 (2018)

Notes on Scoring This response earns no credit (0 points) because it does not identify a quadrilateral with only one set of parallel sides.

• The student draws a quadrilateral that has more than one pair of parallel sides.

156 (2018)


157 (2018)

Notes on Scoring This response earns no credit (0 points) because it does not identify a quadrilateral with only one set of parallel sides.

• The student draws a quadrilateral that has more than one pair of parallel sides.

159 (2018)

Grade 4 Math


Question 39


160 (2018)

Question 39

24343 20512

Points Possible: 1

Content Cluster: Generalize place value understanding for multi-digit whole numbers.

Content Standard: Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. (4.NBT.2)

161 (2018)


• 205,350





163 (2018)

Grade 4 Math


Question 39

Sample Responses

164 (2018)


Notes on Scoring

This response earns full credit (1 point) because it identifies the correct value of “two hundred five thousand, three hundred fifty”.

• The student writes out the number using the correctplace values.

165 (2018)


Notes on Scoring This response earns full credit (1 point) because it identifies the correct value of “two hundred five thousand, three hundred fifty”.

• The student finds a correct equivalent value of 205350.

166 (2018)


Notes on Scoring This response earns no credit (0 points) because it identifies an incorrect value of “two hundred five thousand, three hundred fifty”.

• The student may write the numbers he or she hears when reading the number in word form.

167 (2018)


Notes on Scoring This response earns no credit (0 points) because it identifies an incorrect value of “two hundred five thousand, three hundred fifty”.

• The student may forget to put a 0 as a placeholder in the ten-thousands place.

169 (2018)

Grade 4 Math


Question 44


170 (2018)

Question 44

27946

Points Possible: 1 Content Cluster: Gain familiarity with factors and multiples. Content Standard: Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. (4.OA.4)

171 (2018)

Scoring Guidelines Rationale for First Option: Key – The student correctly identifies a factor of 84. 84 divided by 4 equals 21. Rationale for Second Option: This is incorrect. The student may think 5 is a factor of 84. Rationale for Third Option: Key – The student correctly identifies a factor of 84. 84 divided by 6 equals 14. Rationale for Fourth Option: This is incorrect. The student may think 9 is a factor of 84. Rationale for Fifth Option: Key – The student correctly identifies a factor of 84. 84 divided by 14 equals 6. Rationale for Sixth Option: Key – The student correctly identifies a factor of 84. 84 divided by 21 equals 4.


173 (2018)

Grade 4 Math


Question 47


174 (2018)

Question 47

27399

Points Possible: 1

Content Cluster: Represent and interpret data.

Content Standard: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. (4.MD.4)

175 (2018)

Scoring Guidelines Rationale for Option A: Key – The student identifies the correct line plot by counting the number of times each distance repeats in the table and then matching that amount of x's above the appropriate number on the number line. Rationale for Option B: This is incorrect. The student may only plot the whole number for each distance, forgetting about the fraction portion of the number. Rationale for Option C: This is incorrect. The student may round each distance to the nearest half and plot the results since the tick marks are labeled every 0.5 foot. Rationale for Option D: This is incorrect. The student may round the distances to the nearest whole number and plot those values.


177 (2018)

Grade 4 Math


Question 48


178 (2018)

Question 48

29191 20512

Points Possible: 1


Content Standard: Understand a fraction a/b with a > 1 as a sum of fractions 1/b. (4.NF.3) c. Add and subtract mixed numbers with like denominators, e.g., byreplacing each mixed number with an equivalent fraction, and/orby using properties of operations and the relationship betweenaddition and subtraction.

179 (2018)


• 416




• The correct value (1 point).

181 (2018)

Grade 4 Math


Question 48

Sample Responses

182 (2018)


Notes on Scoring

This response earns full credit (1 point) because it identifies a correct value of the expression.

• The student may add the whole numbers of eachaddend and the fractions of each addend to find thecorrect value of 12

6 and 25

6.

126 + 25

6

= (1 + 2) + �26

+ 56�

= 3 + 76

AND 76 = 11

6

= 3 + 1 16

= 416

183 (2018)


Notes on Scoring This response earns full credit (1 point) because it identifies a correct value of the expression.

• The student may change the mixed numbers to improper fractions and find a correct value equivalent to 41

6.

126 = 8

6 AND 25

6 = 17

6

= 86 + 17

6

= 256

184 (2018)


Notes on Scoring

This response earns no credit (0 points) because it identifies an incorrect value of the expression.

• The student may add the fraction parts of eachaddend without adding the whole numbers.

26 + 5

6 = 7

6

126

+ 256 ≠ 7

6

185 (2018)


Notes on Scoring

This response earns no credit (0 points) because it identifies an incorrect value of the expression.

• The student may add 1+2 to get 3 and 26 + 5

6 to get 7

6.

The student then may replace 76 with 1 instead of 11

6,

and add 3 and 1.

126 + 25

6

= (1 + 2) + �26

+ 56�

= 3 + 76

AND 76 ≠ 1

= 3 + 1

= 4

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Copyright © 2018 by the Ohio Department of Education. All rights reserved.

Documents

Ohio’s State Tests · of operations to perform multi-digit arithmetic. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers,